Hysteresis with Regard to Cassie and Wenzel States on Superhydrophobic Surfaces

Cassie and Wenzel formulas have been used extensively to model the apparent contact angles on rough surfaces. Theoreticians and experimentalists, alike, have noted that such formulas that are based on homogenization theories, while useful, do not capture hysteresis which is determined by the details of contact line motion. Thus, it is of immediate interest to model hysteresis in the context of Cassie and Wenzel type formulas. To address this issue, we consider an ad-hoc generalization of the theory for hysteresis by Joanny and de Gennes. We establish its applicability by reanalyzing the contact angle data from literature for drops in Cassie states on pillar-type roughness geometries. Using this theoretical framework, it is possible to focus on advancing and receding contact line motions separately unlike the analyses of drop motion on inclined planes that quantify the combined effects of advancing and receding fronts. We show how information about the details of contact line motion, during advancing or receding, can be translated into the theoretical framework for hysteresis. The conclusions based on such analyses provide useful physical insights into the energetics of contact line motion and are consistent with experimental observations. We also show that the theoretical framework could be used as a useful guideline to hypothesize the possible mechanisms of pinning/depinning of contact lines that are implicit in the experimental data.